Public Offering of Fund and private equity funds are ways to raise funds. The way to raise money is different.
In an open society, raising money by the public is public offering, while private offering is raising money by small circles.
index funds usually refer to stock funds. It is a passive fund.
the so-called passive index fund is to buy some stocks that follow the synchronous weight of the stock market. It is a passive investment method not to rely on fund managers to actively choose stocks to outperform the market. Because the return on investment of most funds above 95 is statistically lost to the broader market.